1. Field of the Invention
The present invention relates to a method of optical frequency measurement, and more particularly, to a method of measuring the frequency of an unknown laser by varying parameters of optical frequency combs (“frequency combs”).
2. Description of the Related Art
Since Professor Hänsch from Germany applied a femtosecond mode-locked laser to measure the frequency of the D1 line of caesium atoms, mode-locked lasers have drawn more and more attention in the application of optical frequency measurement.
As shown in FIG. 1, in the frequency domain, a mode-locked laser consists of frequency combs with uniform frequency intervals. The frequency of each comb line is equal to an integral multiple of the pulse repetition frequency fr plus an offset frequency fo. That is, the frequency fn of the nth comb line is represented by the following formula:fn=n×fr+fo;where n is a positive integer, fr is the pulse repetition frequency (“repetition rate”), and fo is a carrier-envelope offset frequency (“offset frequency”). Usually, the offset frequency fo is measured with a self-referencing technique. FIG. 2 shows an f-2f self-referencing technique.
However, two possible values fo1 and fo2 smaller than fr will be obtained when the offset frequency fo of the mode-locked laser is detected with the self-referencing technique, and the two offset frequencies satisfy fo1+fo2=fr. According to different definitions, the offset frequency can also be defined as adding an integral multiple of the repetition rate to fo1 and fo2 respectively. Similarly, two beat frequencies fb1 and fb2 can be generated between the unknown laser and the adjacent comb lines (e.g., the nth and the (n+1)th comb lines) of the mode-locked laser, where fb1+fb2=fr. Therefore, the frequency fL of the unknown laser close to the nth comb line is represented by the following formula:fL=n×fr+fo+fb;
where fo=fo1 or fo2, and fb=fb1 or fb2.
The mode order number n of the frequency comb, fo, and fb in the above formula need to be determined so that the frequency fL of the unknown laser can be obtained. The following conventional methods can help to determine n, fo and fb, so as to determine the value of fL. The first method uses historical measured frequencies of the unknown laser, and the frequencies have to be accurate within ±fr/4 to determine the value of n, fo and fb. The second method is to determine the approximate frequency of the unknown laser with a wavelength meter. If the accuracy of the frequency measured by the wavelength meter is within ±fr/4, then the values of n, fo, and fb can be determined. The accuracy of a normal commercial wavelength meter is approximately 2×10−7, and this will cause an uncertainty of about 40 MHz for the frequency measurement of a laser with wavelength of 1550 nm. Therefore, for frequency combs with interval less than 160 MHz, the commercial wavelength meter is not accurate enough to determine the mode number.
The third method is disclosed by Long-sheng Ma et al., and does not need a wavelength meter to determine the mode number n of the frequency comb. According to their method, a frequency comb is applied to measure the beat frequency of an unknown laser under multiple groups of different repetition rates fr and fr′, and the shifted mode number of the beating comb line is recorded when the repetition rate changes. The mode number n of the frequency comb is calculated according to the following formula:n=[±f′−(±fo)+m fr′±fb′−(±fb)]/(fr−fr′);where m is the shifted mode number of the beating comb line when the repetition rate changes from fr to fr′, and fb and fb′ are the beat frequencies between the unknown laser and the beating comb line before and after the repetition rate being adjusted, respectively, and fo, fo′ are the offset frequencies before and after the frequency comb is adjusted. In actual optical frequency measurement, each of fo, fo′, fb, and fb′ has two possible measured values. As the value of each of fo, fo′, fb, and fb′ cannot be determined uniquely, the ± sign in the above formula cannot be determined individually. Therefore, the measurement results of two or more different m values have to be compared and analyzed to identify the correct mode number n of the beating comb line.
The three methods of optical frequency measurement described above require adequate historical measurement data, accurate wavelength meters, and a complicated procedure of comparing multiple measurement results respectively to obtain the frequency of an unknown laser.